Self-error-rejecting multipartite entanglement purification for electron systems assisted by quantum-dot spins in optical microcavities

We present a self-error-rejecting multipartite entanglement purification protocol (MEPP) for N-electron-spin entangled states, resorting to the single-side cavity-spin-coupling system. Our MEPP has a high efficiency containing two steps. One is to obtain high-fidelity N-electron-spin entangled systems with error-heralded parity-check devices (PCDs) in the same parity-mode outcome of three electron-spin pairs, as well as M-electron-spin entangled subsystems (2 ≤ M < N) in the different parity-mode outcomes of those. The other is to regain the N-electron-spin entangled systems from M-electron-spin entangled states utilizing entanglement link. Moreover, the quantum circuits of PCDs make our MEPP works faithfully, due to the practical photon-scattering deviations from the finite side leakage of the microcavity, and the limited coupling between a quantum dot and a cavity mode, converted into a failed detection in a heralded way.

1H R1ρ relaxation dispersion experiments in aromatic side chains

Aromatic side chains are attractive probes of protein dynamic, since they are often key residues in enzyme active sites and protein binding sites. Dynamic processes on microsecond to millisecond timescales can be studied by relaxation dispersion experiments that attenuate conformational exchange contributions to the transverse relaxation rate by varying the refocusing frequency of applied radio-frequency fields implemented as either CPMG pulse trains or continuous spin-lock periods. Here we present an aromatic 1H R1ρ relaxation dispersion experiment enabling studies of two to three times faster exchange processes than achievable by existing experiments for aromatic side chains. We show that site-specific isotope labeling schemes generating isolated 1H–13C spin pairs with vicinal 2H–12C moieties are necessary to avoid anomalous relaxation dispersion profiles caused by Hartmann–Hahn matching due to the 3JHH couplings and limited chemical shift differences among 1H spins in phenylalanine, tyrosine and the six-ring moiety of tryptophan. This labeling pattern is sufficient in that remote protons do not cause additional complications. We validated the approach by measuring ring-flip kinetics in the small protein GB1. The determined rate constants, kflip, agree well with previous results from 13C R1ρ relaxation dispersion experiments, and yield 1H chemical shift differences between the two sides of the ring in good agreement with values measured under slow-exchange conditions. The aromatic1H R1ρ relaxation dispersion experiment in combination with the site-selective 1H–13C/2H–12C labeling scheme enable measurement of exchange rates up to kex = 2kflip = 80,000 s–1, and serve as a useful complement to previously developed 13C-based methods.

Detecting anisotropic segmental dynamics in disordered proteins by cross-correlated spin relaxation

Among the numerous contributions of Geoffrey Bodenhausen to NMR spectroscopy, his developments in the field of spin-relaxation methodology and theory will definitely have a long lasting impact. Starting with his seminal contributions to the excitation of multiple-quantum coherences, he and his group thoroughly investigated the intricate relaxation properties of these “forbidden fruits” and developed experimental techniques to reveal the relevance of previously largely ignored cross-correlated relaxation (CCR) effects, as “the essential is invisible to the eyes”. Here we consider CCR within the challenging context of intrinsically disordered proteins (IDPs) and emphasize its potential and relevance for the studies of structural dynamics of IDPs in the future years to come. Conventionally, dynamics of globularly folded proteins are modeled and understood as deviations from otherwise rigid structures tumbling in solution. However, with increasing protein flexibility, as observed for IDPs, this apparent dichotomy between structure and dynamics becomes blurred. Although complex dynamics and ensemble averaging might impair the extraction of mechanistic details even further, spin relaxation uniquely encodes a protein's structural memory. Due to significant methodological developments, such as high-dimensional non-uniform sampling techniques, spin relaxation in IDPs can now be monitored in unprecedented resolution. Not embedded within a rigid globular fold, conventional 15N spin probes might not suffice to capture the inherently local nature of IDP dynamics. To better describe and understand possible segmental motions of IDPs, we propose an experimental approach to detect the signature of anisotropic segmental dynamics by quantifying cross-correlated spin relaxation of individual 15N1HN and 13C′13Cα spin pairs. By adapting Geoffrey Bodenhausen's symmetrical reconversion principle to obtain zero frequency spectral density values, we can define and demonstrate more sensitive means to characterize anisotropic dynamics in IDPs.

Secular and semi-nonsecular models of cross-polarization kinetics for remote spins: an application for nano-structured calcium hydroxyapatite

The 1H → 31P cross-polarization (CP) kinetics in the nanostructured calcium hydroxyapatite (nano-CaHA) was measured under moderate (5 kHz) magic-angle spinning (MAS) rate. This material was chosen as it contains the distanced 1H–31P spin pairs and the interactions between them are characterized by a relatively low dipolar coupling (b) that could be comparable with the spin-diffusion rates (R). Therefore, the physical legitimacy to use the secular solution of the quantum Liouville–von Neumann equation is doubtful. The semi-nonsecular model of spin dynamics was applied, and the results were compared with those obtained by the secular approach. The comparable results obtained by both models show that the secular model is applicable, with certain reservation, also in the case of |b| ≈ R. The extremely high anisotropy of spin diffusion in the nano-CaHA was deduced. This can be a matter of the applied approach, as the interactions of the 31P spins with the proton bath were neglected in both models. The high anisotropy could also be caused by the physical reasons that stem from the structural and proton diffusion features of CaHA. This material belongs to low-dimensional proton conductors possessing a large motional freedom for protons along OH– chains.

Detecting segmental anisotropic diffusion in disordered proteins by cross-correlated spin-relaxation

Among the numerous contributions of Geoffrey Bodenhausen to NMR spectroscopy his developments in the field of spin-relaxation methodology and theory will definitely have a long lasting impact. Starting with his seminal contributions to the excitation of multiple-quantum coherences he and his group thoroughly investigated the intricate relaxation properties of these “forbidden fruits” and developed experimental techniques to reveal the relevance of previously largely ignored cross-correlated relaxation (CCR) effects, as “the essential is invisible to the eyes”. Here we want to discuss CCR within the challenging context of intrinsically disordered proteins (IDPs) and emphasize its potential and relevance for the studies of structural dynamics of IDPs in the future years to come. Conventionally, dynamics of globularly folded proteins are modeled and understood as deviations from otherwise rigid structures tumbling in solution. However, with increasing protein flexibility, as observed for IDPs, this apparent dichotomy between structure and dynamics becomes blurred. Although complex dynamics and ensemble averaging might impair the extraction of mechanistic details even further, spin-relaxation uniquely encodes a protein’s structural memory, i.e. the temporal persistence of concerted motions and structural arrangements. Due to significant methodological developments, such as high-dimensional non-uniform sampling techniques, spin-relaxation in IDPs can now be monitored in unprecedented resolution. Not embedded within a rigid globular fold, conventional 15N spin probes might not suffice to capture the inherently local nature of IDP dynamics. To better describe and understand possible segmental motions of IDPs, we propose an experimental approach to detect the signature of diffusion anisotropy by quantifying cross-correlated spin relaxation of individual 15N1HN and 13C'13Cα spin pairs. By adapting Geoffrey Bodenhausen’s symmetrical reconversion principle to obtain zero frequency spectral density values we can define and demonstrate more sensitive means to characterize segmental anisotropic diffusion in IDPs.

Spin-1/2 one- and two- particle systems in physical space without eigen-algebra or tensor product

A novel representation of spin 1/2 combines in a single geometric object the roles of the standard Pauli spin vector and spin state. Under the spin-position decoupling approximation it consists of the ordered sum of three orthonormal vectors comprising a gauge phase. In the one-particle case the representation: (1) is Hermitian; (2) is oriented due to ordering; (3) reproduces all standard expectation values, including the total one-particle spin modulus A; (4) constrains basis opposite spins to have same orientation; (5) allows to formalize irreversibility in spin measurement. In the two-particle case: (1) entangled spin pairs have opposite orientation and precisely related gauge phases; (2) the dimensionality of the spin space doubles due to variation of orientation; (3) the four maximally entangled states are naturally defined by the four improper rotations in 3D: reflections onto the three orthogonal frame planes (triplets) and inversion (singlet). The cross-product terms in the expression for the squared total spin of two particles relates to experiment and they yield all standard expectation values after measurement. Here spin is directly defined and transformed in 3D orientation space, without use of eigen algebra and tensor product as in the standard formulation. The formalism allows working with whole geometric objects instead of only components, thereby helping keep a clear geometric picture of ‘on paper’ (controlled gauge phase) and ‘on lab’ (uncontrolled gauge phase) spin transformations.

Spin-1/2 one- and two- particle systems in physical space without eigen-algebra or tensor product

A new representation for spin 1/2 in the even 3D subalgebra of the spacetime algebra (STA) combines in a single geometric object the roles of the standard Pauli spin vector and spin state. It is a vector quantity comprising a gauge phase. In the one-particle case the representation (1) is Hermitian; (2) chiral; (3) reproduces all standard expectation values, including the total one-particle spin modulus ; (4) constrains a spinor basis representing opposite spins to preserve handiness (chirality); (5) the gauge phase allows to explicitly formalize irreversibility in spin measurement. In the two-particle case it (1) identifies entangled spin pairs as having opposite handiness and precise gauge phase relations; (2) doubles the dimensionality of the spin space due to variation of handiness; (3) the four maximally entangled states are naturally derived by pairing spins that are reflections (triplets) and inversions (singlet) of each-other. The cross-product terms in the expression for the squared total spin of two particles can be affected by experiment and they yield the standard expectation values after measurement. Here I directly define and transform spin in 3D orientation space, without invoking concepts like abstract Hilbert space and tensor product as in the standard formulation. The STA formalism allows working with whole geometric objects instead of only components, thereby helping keep a clear geometric picture of ‘on paper’ (controlled gauge phase) and ‘on lab’ (uncontrolled gauge phase) spin transformations.

Synthesis of 13C/19F/2H Labeled Indoles for Use as Tryptophan Precursors for Protein NMR Spectroscopy

Synthesis of indoles labeled with 13C-1H and 13C-19F spin pairs is described. All syntheses utilize inexpensive carbon-13C dioxide as the 13C isotope source. Ruthenium-mediated ring-closing metathesis is the key step...